Space of modular forms of level 285, weight 2, and Character 285.q

• Label: 285.2.q
• Level: $285$
• Weight: $2$
• Character orbit: 285.q
• Rep. character: $\chi_{285}(164,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	72	72	0
Eisenstein series	16	16	0

Trace form

\( 72 q + 26 q^{4} - 10 q^{6} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(285, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
285.2.q.a	$285$	$2$	285.q	285.q	$6$	$4$	$2$	$2.276$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(-3\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(2+\beta _{3})q^{3}+(1+3\beta _{1}+\cdots)q^{4}+\cdots\)
285.2.q.b	$285$	$2$	285.q	285.q	$6$	$4$	$2$	$2.276$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(3\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-2-\beta _{3})q^{3}+(1+3\beta _{1}+\cdots)q^{4}+\cdots\)
285.2.q.c	$285$	$2$	285.q	285.q	$6$	$8$	$4$	$2.276$	8.0.3317760000.3	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(-2+2\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
285.2.q.d	$285$	$2$	285.q	285.q	$6$	$56$	$28$	$2.276$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$